DIAGNOSIS Standing water points to a drain path blockage. The most common spot is in the filter area or the drain hose, not necessarily a failed pump.
FIX 1. Check and clean the filters as described in the previous answer. A clogged filter is the number one cause. 2. Check the drain hose under the sink. Make sure it has a high loop (a section of hose secured up under the counter) to prevent sink water from back-siphoning into the dishwasher. 3. Disconnect the drain hose from the sink drain or garbage disposal. Have a bucket and towels ready. Detach the hose and check for a clog. Blow through it or run water from a faucet through it to clear any debris.
IF THAT DIDN'T WORK If the hose is clear, the issue might be at the connection to the garbage disposal. If you have one, check the disposal's drain inlet. There's often a plastic knockout plug that needs to be removed. Even if it was removed during install, food can build up there. Use a hex key or a screwdriver to clear that inlet from the disposal side.
HEADS UP Never use chemical drain openers in your dishwasher. They can damage rubber seals and hoses. Always go for mechanical clearing first.